A New Version of the Generalized Krätzel–Fox Integral Operators

Abstract

This article deals with some variants of Krätzel integral operators involving Fox’s H-function and their extension to classes of distributions and spaces of Boehmians. For real numbers a and b > 0 , the Fréchet space H a , b of testing functions has been identified as a subspace of certain Boehmian spaces. To establish the Boehmian spaces, two convolution products and some related axioms are established. The generalized variant of the cited Krätzel-Fox integral operator is well defined and is the operator between the Boehmian spaces. A generalized convolution theorem has also been given.

Keywords

• <i>H</i>-function
• kernel method
• Krätzel function
• Krätzel operator
• distribution space
• Boehmian space